Donald Trump said his son Donald Trump Jr. will not run for mayor of New York City, apparently putting an end to speculation that his son encouraged last week.

Appearing on CNN's "State of the Union" on Sunday, the eldest son of GOP presidential nominee said he's open to running for public office one day, telling the program, "I never like to rule anything out . . . If I can do that as a service to our country, I'd love to do it."

However, Trump senior, appearing on Fox News' "Hannity" program Monday night said his son is "not going to run for mayor. No, he has no intention of doing that. He wouldn't want to do that."

Hannity countered that Trump Jr., an executive vice president at the Trump Organization, said he was leaving the possibility open, but Trump reiterated that he did not believe his son would run.

"Well, he'll leave it open. Running for mayor of New York City — all right, I don't see that happening. I don't think that'll happen," Trump said, but he did praise his son's RNC speech.

"It was really the first major speech he's ever made, and he spoke like he's been doing it all his life."

Trump Jr.'s address at the Republican National Convention earned praise and according to Politico, there was speculation that a political career could be in his future.

During his RNC speech, Trump Jr. said his father's "true gift as a leader is that he sees the potential in people that they don't even see in themselves."